as played i think fold flop or call both r ok
the odds is so good and we r ip but as u said checking raise in this multiway pot by mp could be very strong and bb could have a draw
its reallly difficult to play on any turn if mp bets

Flop: Just fold it while also having people behind you to act, you could already be against JT or whatsoever and maybe just going for the FH and that's it might not even have the implied odds. It was just a min-raised pot, not worth overplaying your hand.